Earthquakes and Structures, Vol. ????, No. ???? (????) 1–20 DOI: http://dx.doi.org/???? 1 Parametric seismic evaluation of highway overpass bridges in moderate seismic areas J´ ozsef Simon* 1 and L´ aszl´ o Gergely Vigh 1a 1 Department of Structural Engineering, Budapest University of Technology and Economics, Budapest, M˝ uegyetem rkp. 3-5.,H-1111, Hungary (Received ????, Revised ????, Accepted ????) Abstract. Prior to modern seismic provisions, several bridges were not designed for seismic actions in moderate seismic areas. Precast multi-girder and slab bridges are typical highway overpass struc- tures, they have a significant contribution to national bridge stocks. Since the seismic behavior is questionable, a preliminary parametric study is conducted to determine critical configurations and components. The results indicate that the behavior of the abutments, backfill soil, superstructure and foundation is normally satisfactory; however, the superstructure-abutment joints are critical for both single and multi-span bridges, while the piers are also critical for longer multi-span configurations. The parametric results provide a solid basis both for detailed seismic assessment and development of design concepts of newly built structures in moderate seismic zones. Keywords: Seismic analysis; parametric analysis; multi modal response spectrum analysis; seismic performance; bridge engineering; moderate seismicity 1. Introduction In modern seismic codes (e.g. CEN (2008a, b), BSSC (2009)) seismic design of bridges is prescribed in moderate seismic regions; however a large portion of existing structures were non-seismically designed in these areas due to the lack of proper seismic provisions prior to the introduction of modern standards. Several studies (Choi and Jeon 2003, Nielson 2005, Ramanatan et al. 2012, Zsarn´ oczay et al. 2014, Simon et al. 2015) have shown that existing road bridges may be vulnerable even in moderate seismic regions. This high vulnerability stems not only from the lack of seismic design and detailing, but also from the fact that the seismic hazard has been recently revised in many countries of moderate seismicity (e.g. Austria, Belgium, Czech Republic, Germany, Slovakia, Slovenia, Switzerland). New seis- mic hazard maps were created showing an increased hazard (Solomos et al. 2008), therefore additional seismic demands are imposed on the structures compared to the previous stan- dards. This latter issue is a subject of a huge debate among civil engineers and authorities; *Corresponding author, Ph.D., E-mail: [email protected]a Ph.D., E-mail: [email protected]Copyright c ???? Techno-Press. Ltd. http://www.techno-press.org/?journal=sem&subpage=8 ISSN: 1225-4568(Print), 1598-6217(Online)
Parametric seismic evaluation of highway overpass bridges inmoderate seismic areas
Jozsef Simon*1 and Laszlo Gergely Vigh1a
1Department of Structural Engineering, Budapest University of Technology and Economics, Budapest,Muegyetem rkp. 3-5.,H-1111, Hungary
(Received ????, Revised ????, Accepted ????)
Abstract. Prior to modern seismic provisions, several bridges were not designed for seismic actionsin moderate seismic areas. Precast multi-girder and slab bridges are typical highway overpass struc-tures, they have a significant contribution to national bridge stocks. Since the seismic behavior isquestionable, a preliminary parametric study is conducted to determine critical configurations andcomponents. The results indicate that the behavior of the abutments, backfill soil, superstructure andfoundation is normally satisfactory; however, the superstructure-abutment joints are critical for bothsingle and multi-span bridges, while the piers are also critical for longer multi-span configurations.The parametric results provide a solid basis both for detailed seismic assessment and development ofdesign concepts of newly built structures in moderate seismic zones.
In modern seismic codes (e.g. CEN (2008a, b), BSSC (2009)) seismic design of bridges isprescribed in moderate seismic regions; however a large portion of existing structures werenon-seismically designed in these areas due to the lack of proper seismic provisions prior tothe introduction of modern standards. Several studies (Choi and Jeon 2003, Nielson 2005,Ramanatan et al. 2012, Zsarnoczay et al. 2014, Simon et al. 2015) have shown that existingroad bridges may be vulnerable even in moderate seismic regions. This high vulnerabilitystems not only from the lack of seismic design and detailing, but also from the fact thatthe seismic hazard has been recently revised in many countries of moderate seismicity (e.g.Austria, Belgium, Czech Republic, Germany, Slovakia, Slovenia, Switzerland). New seis-mic hazard maps were created showing an increased hazard (Solomos et al. 2008), thereforeadditional seismic demands are imposed on the structures compared to the previous stan-dards. This latter issue is a subject of a huge debate among civil engineers and authorities;
the structural safety of existing structures against severe earthquake-induced damage andultimately collapse is questionable. Therefore, in these regions, where seismic design is prac-tically non-existent, there is a need for a fast and overall, nationwide seismic performanceevaluation of the most important bridge types to provide: 1) insight on the seismic risk forthe authorities; 2) information on the seismic behavior and the critical bridge configurationsand components for practicing engineers, which can be useful in case of a new bridge design.
The most common structural types on highways are the precast multi-girder (PMG)and reinforced concrete slab bridges; these typologies are widely employed in several regionsaround the world (Connal 2014, Nielson 2005, Pinto and Franchin 2010). For instance,evaluation of a representative bridge database (HTA 2016) shows that besides bridges withconventional bearings, the number of PMG and slab bridges with monolithic joints has acontribution of more than 70% to the national bridge stock.
There are a few examples of comprehensive seismic performance evaluation of highwaybridges (e.g. in the US (Nielson 2005), Italy (Borzi et al. 2015), Greece (Moschonas et al.2009), Turkey (Avsar et al. 2015)), however there are several reasons why the results of thesestudies cannot be adapted: 1) the higher seismicity of the mentioned countries in Europeresults in different design traditions, therefore structural characteristics and details; 2) PMGand slab bridges examined in this study are dominantly continuous and built with monolithicjoints, while simply supported versions are more preferred in the mentioned regions; 3) thestudies do not cover all the possible bridge configurations; 4) the vulnerability depends on theapplied seismic actions, which should be determined considering the seismic characteristicsand site properties, thus results are expected to differ in moderate seismic zones.
The objective of this study is to investigate the seismic performance of typical PMG andslab bridges. A parametric seismic analysis and standard evaluation per the EC8 standardare carried out. Main variable parameters (number of spans, span of single bay, deck width,pier height) are selected to represent a wide range of different configurations that can befound on highways. Based on the results, critical layouts and components are determined,demand-capacity ratios of bridge components are calculated. A possible application of theparametric results is also illustrated with an example: a nationwide seismic performanceevaluation is performed for Hungarian road bridges; a first estimation is given for the numberof critical bridges considering the whole bridge stock.
2. Description of the examined bridge configurations
Both PMG and slab bridges are constructed with monolithic joints of which there are twotypical types: 1) piers are joined directly to the reinforced concrete deck (Fig. 1a) in case ofslab bridges; 2) vertical reinforcement is applied at the pier cap (Fig. 1b) of PMG bridgesand at the abutments (Fig. 1c) of PMG and slab bridges to transfer lateral forces only.Type 1 joints can be characterized with complex behavior transferring both shear forces andbending moments from the superstructure to the piers, while the behavior of Type 2 jointsis simpler. Since only shear reinforcement is applied, they can be characterized with semi-rigid flexural behavior. The flexural stiffness is negligible compared to that of the adjacentstructural elements, thus it is best approximated as hinged (Fennema et al. 2005).
Seismic evaluation of highway overpass bridges 3
Fig. 1 Monolithic joint types. a) Piers are joined directly to the deck (Type 1 ; slab bridges). Shearreinforcement is applied between: b) the deck and the pier cap (Type 2 ; PMG bridges); c) the deckand the abutment (Type 2 ; both PMG and slab bridges).
h: function of span length (L)Pier cap cross section
1.2
1.0
No. of spans: 1-4Span length L = 5-30 m
0.6
0.9
D=80 cm piles in two rows
D=80 cm piles in one row
Pier cross sectionD=80 cm piles in one row
D=80 cm piles in two rows
b)
?12/150 stirrups16?20 long. reinf.
Pile D = 80 cm Pier
Type 2 joint
w
X
Z
Y
Z
YX
Y
X
Y
X
h=-0.0004 (L-5) + 0.035 (L-5) + 0.4 [m]2
Pie
r h
eig
ht
=
2-1
0 m
Type 2 joint Type 2 joint Type 2 joint
Fig. 2 General layout of PMG bridges: a) side-view of the bridge; b) typical cross section; c) appliedpile foundation arrangements for different bridge widths.
Fig. 2a shows the general layout of PMG bridges. They are constructed as follows. In thefirst construction steps, the substructure is created (piles, pile cap, abutments and piers, andfinally the pier cap beam); vertical reinforcements are extended from the abutment and piercap. Precast beams are placed on the pier cap beam and on the abutments. The last step isto position the reinforcements of the deck, then the monolithic joints and the concrete deckare constructed with cast-in-situ concrete. Typical shear reinforcements of the monolithicType 2 joints are φ16/150 at the abutment and 2φ16/150 at the piers. The structural heightof the girder is determined as the function of the span length (an equivalent slab is consideredtaking into account stiffness and mass properties; see Fig. 2b). Additional permanent loadof the superstructure is 750 kg/m railing and 400 kg/m2 pavement. Piers are constructedas multi-column bents with 3-4 m transverse distance. Longitudinal reinforcement ratio istypically 1%, while minimal shear reinforcement (mostly φ12/150) is applied due to the lowshear forces in conventional design situations (e.g. traffic loads).
Since these bridges are highly popular on highways, cross section of the piers (0.6 m x 0.9m) and the pier cap (1.0 m x 1.2 m) and the dimensions of the abutments (1.0 m x 2.0 m) aremore or less the same for all structures for the efficient reusability of formwork. Accordingly,pier and cap beam cross-section, abutment geometry are considered fixed during the studies.
4 J. Simon and L.G. Vigh
The foundation system is mostly pile foundation, the assumed layouts for different deckwidths are shown in Fig. 2c. The input parameters of the parametric study are presented inTable 1 where the notations for different configurations are also indicated (e.g. a 14 m wide,3-span bridge with 6 m pier height and 20 m span length is referred to as W14S3P06L20).
Table 1 Input parameters for the parametric study and notations for different configurations.
Slab bridges are cast-in-situ monolithic reinforced concrete structures commonly con-structed as highway overpass bridges along with PMG bridges. Their construction requiresstand- and formwork, thus the construction time is longer than in case of PMG bridges. Thegeneral layout is shown in Fig. 3a. The global geometry is usually the same as of PMGbridges, thus the examined configurations and the parametric space are assumed to be thesame in this study (see Table 1). Nonetheless, fundamental differences affecting the behaviorof slab bridges should be highlighted. Note that there is no pier cap, piers are connecteddirectly to the deck with a monolithic joint which can transfer not only shear forces butalso bending moments (monolithic joint Type 1 ). However, the joints at the abutments areconstructed with one layer of vertical bars only, characterized by a similar behavior as PMGbridge joints (monolithic joint Type 2 ). The stiffness and mass of the deck is calculated con-sidering typical slab bridge cross-sections for different deck widths (Fig. 3b). The structuralheight is determined as the function of span length.
a)
h: function of span length (L)
No. of spans: 1-4Span length L = 5-30 m
0.6
0.9
D=80 cm piles in two rows
D=80 cm piles in one row
Pier cross sectionD=80 cm piles in one row
D=80 cm piles in two rows
b)
?12/150 stirrups16?20 long. reinf.
hp
h bph = L/18 hp = 0.25 m
W = 8 m >> bp = 1.0 m; W = 14 m >> bp = 1.5 m; W = 20 m >> bp = 2.0 m
w
X
Z
Y
Z
Type 2 joint Type 1 joint Type 1 joint Type 2 joint
Pie
r hei
ght
=
2-1
0 m
Fig. 3 General layout of SLAB bridges: a) side-view of the bridge; b) general cross-section.
3. Applied procedure for parametric seismic analysis
State of the art seismic vulnerability evaluation techniques are based on analytical fragilitycurves (Billah and Alam 2015). Damage evaluation is necessary for estimating loss and eco-nomic consequences, however, to estimate the occurrence probability of different damagelevels, each bridge has to be modeled with high fidelity and reliable input values (Simon andVigh 2016). In typical moderate seismic regions, seismic design is practically non-existent.Therefore, prior to detailed analyses, it is advantageous to perform a preliminary study
Seismic evaluation of highway overpass bridges 5
to highlight critical configurations, and most importantly to give an estimation of possiblycritical structures, enabling the authorities to make decisions about further actions.
Several simplified vulnerability assessment methodologies have been worked out basedon bridge inspection without complex calculations (Kibboua et al. 2014). These method-ologies (Kawashima and Unjoh 1990, Gilbert 1993, OFROU 2005, Marchand et al. 2006)apply a scoring system and vulnerability parameter, which are determined considering themain aspects of bridge vulnerability: intensity of earthquake, soil conditions, main structuralattributes etc. The disadvantage of this approach is two-fold: 1) it requires comprehensiveinspection of each bridge (which can be a time-consuming procedure); 2) it is based on re-gression analysis on bridge damage data, thus the reliability of the evaluation is questionable,especially if bridges with significantly different main structural attributes are investigated.
A transitional approach between detailed fragility analysis and simplified inspection-based evaluation is the application of a simplified yet informative analysis procedure. Themain structural attributes (e.g. pier height or span length) of PMG and slab bridges arediverse, thus a parametric evaluation is necessary to determine which configurations maybe vulnerable and require further detailed analysis. Accounting for these requirements, anintensity based approach is adopted in this study, considering a typical moderate PGAvalue of 1.5 m/s2 related to the EC8-1 non-collapse criteria (PGA hazard is computed at10% exceedance rate in 50 years). Time-efficient multi modal response spectrum analysis(MMRSA) is used to compute seismic demands. Although MMRSA cannot capture non-linear behavior, the short computational time ensures to cover a wide multi-dimensionalparametric field, and provides insight about the governing seismic demands.
An OpenSees procedure is written by the authors (Simon and Vigh 2014) to carry outMMRSA per EC8-1. The procedure calculates the necessary number of modes (i.e. the 90%modal mass rule is applied), then spectrum analysis is carried out. Modes are combinedwith the Complete Quadratic Combination method, while the combination of results ofeach direction is based on the Square Root of the Sum of the Squares approach. Theapplied acceleration response spectrum (Fig. 4) assumes a reference soil type C and Type 2spectral shape per EC8-1, well reflecting typical circumstances. The bridges are considered asordinary bridges of normal importance, thus an importance factor of 1.0 is used to determinethe seismic load. A behavior factor q=1.0 is applied as it is suggested by EC8-2 for bridgeswith a deck connected to both abutments with monolithic joints.
0 0.5 1 1.5 2 2.5 30
2
4
6
Vibration period [s]
Sp
ect
ral a
cce
lera
tio
n [
m/s2
]
Tc
Fig. 4 Applied standard Type 2 acceleration response spectrum (PGA = 1.5 m/s2, soil type C, q=1).
6 J. Simon and L.G. Vigh
4. Numerical model
A three dimensional beam-element model (Fig. 5) is created in OpenSees (McKenna etal. 2010). The superstructure, piers and abutments are modeled with two-node 3D beamelements with 6 degree of freedoms (DOFs) per node, with elastic behavior due to thelinear nature of the analysis method. The beam elements are placed in the center of mass,eccentricity between the member axes is bridged over with rigid elements. A typical meshsize of 0.25 m results in approximately from some 100 to 1000 nodes (600-6000 DOFs), whichis found sufficient to efficiently achieve results with an acceptable accuracy. The mass of thestructure and the additional dead load (pavement, rails etc.) are lumped at nodes.
Although, non-linear elements could be applied with the help of effective stiffness andequivalent damping (CEN 2008b), in this case an iterative procedure is needed, besides, thelack of knowledge on the actual cyclic behavior of the components questions the reliabilityof the results. Nonetheless, effective pier stiffness (∼50-65% of the uncracked stiffness) isaccounted for, where concrete Young modulus of 30 GPa is assumed.
Z
Y
X
SuperstructureElasticBeamElement
Lumped mass
PiersElasticBeamElement
Cap beamElasticBeamElement
Detail A
Superstructure-pier cap connection
Detail B
Soil-structure interaction/Pile foundation
AbutmentElasticBeamElement
Detail C
Abutment-backfill interaction
Translational springs: X-Y-Z direction
Rigid link
Fixed node
Rotational springs: X-Y-Z direction
Rigid link
Translational springs: X-Y-Z
Superstructure-pier cap connection
Rigid link
Rigid link
(ZeroLength elements)
PiersElasticBeamElement
SuperstructureElasticBeamElement
Cap beamElasticBeamElement
Detail A
Detail B
Detail C
Fixed nodes
AbutmentElasticBeamElement
Translational springs: X-Y-Z direction Fixed nodeRotational springs: X-Y-Z direction
Translational springs
X direction
(ZeroLength elements)
(ZeroLength elements)
(ZeroLength elements) (ZeroLength elements)
(ZeroLength elements)
Fig. 5 Numerical model.
The monolithic joints are modeled with linear springs (Fig. 5 detail A), where a stiffness of1013 N/m is used to model fully rigid conditions. Monolithic Type 1 joints transfer both shearforces and bending moments, thus all DOFs are set to be fixed; while the hinged behavior ofType 2 joints are taken into account by assigning fixed condition to three translational (ux,uy, uz) and two rotational DOFs (φx, φz) only.
The dynamic impedance of the soil-foundation system can be approximated through as-semblies of springs, dashpots and fictitious masses (Wolf 1985). In this study, a conservativeapproach is followed, both radiation and material damping of the soil is neglected, whilelinear springs are used to take into consideration the translational and flexural stiffness ofthe pile foundation (Fig. 5 detail B). The vertical stiffness of an individual pile is determined
Seismic evaluation of highway overpass bridges 7
as the initial stiffness of a simplified tri-linear behavior, representing the combined behaviorof skin friction and tip resistance; the horizontal stiffness is estimated according to EC8-5Annex C (CEN 2009a). The translational and rotational stiffness of the foundations are cal-culated directly from the vertical and horizontal stiffness of the individual piles consideringthe actual layout of the pile foundation system.
Since PMG and slab bridges are built with monolithic joints, the seismic resistance isprovided by both piers and abutments. In this case, the use of lower and upper boundestimates of the soil stiffness is recommended to obtain conservative demands for both theinternal forces and deformations. Table 2 illustrates representative stiffness values consid-ering the Young modulus of the soil as either 10 MPa (lower) or 100 MPa (upper) (typicalrange from soft to stiff clay and from loose to compact sand).
Table 2 Stiffness values of the foundation springs. kx, ky and kz denote translational stiffness alongthe x, y and z axis (see Fig. 5); while kxx, kyy, kzz represent rotational stiffness values about thesame axes, respectively.
The backfill soil under compression provides extra support in addition to the stiffnessof the abutment. Its influence on the seismic response can be dominant in the longitudinaldirection. As part of the Caltrans seismic research program, full-scale abutment field experi-ments were conducted (Maroney 1995). The test results showed hyperbolic force-deformationbehavior of the abutment-backfill soil system subjected to monotonic longitudinal loading.This behavior is approximated in the model with linear springs (due to the linear nature ofthe analysis method) using the initial stiffness of the backfill soil. One end of the springs isattached to the nodes of a rigid grid modeling the surface of the abutment; the other endis attached to fixed nodes (Fig. 5 detail C). The initial stiffness of the hyperbolic curve iscalculated per Caltrans (2013) from an initial stiffness value (Ki) determined for the entirewidth (w) of the bridge. The stiffness is adjusted to a typical backwall height (H=2m) andlumped to the abutment surface nodes proportionally to the corresponding areas (A):
K0 = (Ki · w · (H/1.7m))/A (1)
MMRSA cannot take into account that the backfill soil works only in compression, itassigns the same initial stiffness in the tension zone as well. The examined bridges have bothlongitudinal and transverse axes of symmetry, thus the longitudinal vibration mode withmovements toward one abutment is identical to the one moving toward the other abutment.For this reason, during linear MMRSA spring elements are applied at only one of the abut-ments to model the effect of the backfill soil only in compression. The simplified modelingof soil-structure interactions is sufficient for present preliminary study, more advanced anddetailed modeling can be found in (Simon and Vigh 2016).
8 J. Simon and L.G. Vigh
5. Results
5.1 Modal analysis
Typical vibration modes of different PMG configurations are illustrated in Fig. 6a-d.The modal analysis results show the high stiffness and thus low fundamental periods ofthese structures. In the case of shorter, less flexible bridges (see shorter span lengths in Fig.6e), the fundamental period is often lower than the Tc corner period (see Fig. 4), thus itfalls onto the plateau of the applied response spectrum. This indicates that high base shearforces are expected and that these bridges are possibly vulnerable against seismic actions.
5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
0.6
Span length [m]
T0
[s]
P02
P04
P06
P08
P10
Soil type D
Soil type A,B,C
e)
a) b)
c) d)
T0 = 0.11 s T0 = 0.35 s
T0 = 0.19 s T0 = 0.30 s
Fig. 6 First vibration modes and fundamental periods for different typical layouts of W14P06 bridges.a) S2L10; b) S2L25; c) S4L10; d) S4L25. e) Fundamental periods for W14S4 bridges (TC periods:red dashed line).
5 10 15 20 25 300
0.1
0.2
0.3
0.4
0.5
Span length [m]
T0
[s]
P02
P04
P06
P08
P10
Soil type A,B,C
Soil type D
b)a)
Mode 3 - T0 = 0.30 s
Mode 4 - T0 = 0.27 s
Mode 5 - T0 = 0.21 s
Fig. 7 a) Typical vibration modes and fundamental periods for the W08S4P06L30 configuration. b)Fundamental periods of W14S4 configurations (TC periods: red dashed line).
Fig. 7a shows typical vibration modes of the W08S4L30P06 slab configuration, illustrat-ing the high level of interaction between the longitudinal and vertical vibrations; pier shearand bending also occur during vertical vibration due to the monolithic joint Type 1. Simi-larly to PMG bridges, slab bridges can also be characterized by high vibration frequencies(Fig. 7b), the fundamental periods are often on the plateau of the applied spectrum.
Seismic evaluation of highway overpass bridges 9
5.2 Effect of the soil-structure interaction
Since PMG and slab bridges are built with monolithic joints, the seismic resistance isprovided by both piers and abutments, thus the soil-structure interaction (SSI) can sig-nificantly influence the seismic behavior. In this case, the use of upper and lower boundestimates of the soil stiffness (see Table 2) is recommended to obtain conservative demandsfor each bridge component. The effect of the backfill soil is also investigated with two differ-ent stiffness values (Ki = 28.7 kN/mm/m and 14.35 kN/mm/m) per Caltrans (2013). Threecases are examined: in each case one of the three components (backfill soil - 100, abutmentfoundation - 010, pier foundation - 001 ) is characterized with its higher, while the other twowith their lower stiffness values. In Table 3 and 4 representative results are illustrated fortwo different layouts for PMG and slab bridges, respectively.
Table 3 Sensitivity of MMRSA results to different SSI stiffness. P06L20 PMG bridges: a) W08S2; b)W20S4. ∆ denotes the relative difference between maximum and minimum values in %.
a) Pier internal forces Abutment joint Pier joint Backfill Disp.
Code Vx Vy Mx My Fx Fy Fx Fy σ dx dy[kN] [kN] [kNm] [kNm] [kN] [kN] [kN] [kN] [kPa] [mm] [mm]
Table 4 Sensitivity of MMRSA results to different SSI stiffness. P06L20 slab bridges: a) W08S2; b)W20S4. ∆ denotes the relative difference between maximum and minimum values in %.
a) Pier internal forces Abutment joint Pier joint Backfill Disp.
Code Vx Vy Mx My Fx Fy Fx Fy σ dx dy[kN] [kN] [kNm] [kNm] [kN] [kN] [kN] [kN] [kPa] [mm] [mm]
Conservative pier internal forces and pier joint shear forces are obtained considering the
10 J. Simon and L.G. Vigh
pier foundation as the stiffest element of the SSI (code: 001 ). The same behavior can beobserved in case of the abutment-backfill soil system. The increased stiffness of these com-ponents (code: 100 or 010 ) can slightly affect the abutment joint shear forces; while thepassive earth pressure is significantly dependent on the stiffness of the backfill soil (code:100 ). Observing the girder displacements, both longitudinal and transverse movements arecontrolled by the stiffness of the abutment foundation (code: 010 ). The results for slabbridges are similar to the ones observed in case of PMG bridges, however note that pierinternal forces are increased compared to PMG bridges with the same configurations. Asconfirmed by Table 3 and 4, using non-conservative variation may lead to ∼60% underesti-mation of specific demands. Therefore, in this study analyses are carried out with all thethree variations to calculate conservative results for each component.
5.3 Calculated demands
5.3.1 SuperstructureIn Fig. 8b vertical girder bending moments of the W14S4P06L25 PMG configuration are
illustrated (note that seismic demands obtained with MMRSA are always positive due tothe combination of modal responses, however negative signed values are also valid becauseof the bi-directional nature of earthquakes). The moments from dead load are dominantlysagging due to the composite construction technology (considerable dead load is carried bythe simply supported girders, since continuity is created after the hardening process of theconcrete slab). A significant contribution can be observed from the longitudinal vibration(EQX) compared to the vertical one (EQZ). This can be explained as follows. Horizontalforces are transferred with eccentricity from the substructure. The longitudinal movementof the piers can develop only if the girders are bent (Fig. 8a). The high stiffness of the wholesystem implies significant bending moments; besides, the intensity of the horizontal groundmotion is usually higher.
As for slab bridges, vertical bending moments illustrated in Fig. 9a shows that thecontribution of the longitudinal vibration (EQX) is still as significant as the vertical one(EQZ). However, the total seismic effect is negligible compared to the dead load in this case.
0 10 20 30 40 50 60 70 80 90−1.5
−1
−0.5
0
0.5
1x 10
4
Bridge length [m]
SS My [kNm]
Dead loadEQXEQZ
a)
b) 5 10 15 20 25 300
0.2
0.4
0.6
0.8
1
Span length [m]
EQ/ULS bending moment ratios
S1 − EC (+)S1 − ÚT (+)S4 − EC (+)S4 − ÚT (+)S4 − EC (−)S4 − ÚT (−)
c)
Fig. 8 a) Dominant vibration mode in the longitudinal direction. b) Vertical superstructure (SS)bending moments (My) of the W14S4P06L25 PMG configuration. c) EQ/ULS My ratios for W14P06PMG bridges.
Seismic evaluation of highway overpass bridges 11
5 10 15 20 25 300
0.2
0.4
0.6
0.8
1
Span length [m]
Ver
tica
l ben
din
g m
om
ent
EQ/U
LS
S1 − ÚT (+)S4 − ÚT (+)S4 − ÚT (−)
b)
0 10 20 30 40 50 60 70 80 90−2
−1
0
1
2
3x 104
Bridge length [m]
SS M
y [k
Nm
]
Dead loadEQXEQZ
a)
Fig. 9 a) Vertical bending moments (My) of the superstructure (W14S4P06L25 slab configuration).b) Ratios of vertical bending moments calculated in EQ and ULS for W14P06 slab bridges.
Evaluation of the superstructure is carried out as follows. Even though the girders arenot designed for seismic action, they should withstand the demands in Ultimate Limit State(ULS). Internal forces are determined both in ULS and in seismic combination (EQ). InFig. 8c, ratios of maximum bending moments of PMG bridges, calculated in accordancewith the former Hungarian standard UT (2004) and with EC0 (CEN 2011) are shown. Thetwo standards differ in the partial factor of the dead load (1.1 and 1.35 in UT and EC,respectively) leading to a significant difference in the superstructure capacity. The inducedadditional safety per EC results in higher capacity and better seismic performance. TheEQ/ULS ratios indicate that single span bridges are less vulnerable; and even for multi-spanbridges the critical ratio of 1.0 (failure of the girders) for either sagging (+) or hogging (-)moments is not reached. The low vilnerability of slab bridges can also be confirmed, Fig. 9bshows that the EQ/ULS ratios (calculated per UT) remain under 0.7.
Transverse bending moments of the superstructure may be higher than those from ULS,however the flexural capacity is still an order of magnitude greater, failure is not expected.For instance, the compressive stress in the external concrete fiber is around 2-5 MPa in caseof both PMG and slab bridges.
5.3.2 Monolithic jointsIn Fig. 10a-d resultant joint shear forces are shown. Increasing demands with increasing
span length is a general tendency due to the higher applied mass. Shear forces are higher atthe superstructure-abutment joint as a result of the relatively high stiffness of the abutment-backfill soil system. At the abutment joint (Fig. 10a), increase is observed at shorter piers(<4 m), while the tendency is reversed at the pier joint (Fig. 10b). The effect of the deckwidth is illustrated in Fig. 10c showing that the results are nearly the same for 14 m and 20m width, while slightly increased demands are obtained for 8 m.
To evaluate critical configurations, the shear resistance of the joints (Ru) is determinedwith the formula presented in (Psycharis and Mouzakis 2012):
Ru = 1.1 · n ·D2 ·√fcd · fsd/γR (2)
12 J. Simon and L.G. Vigh
5 10 15 20 25 300
2
4
6
8x 10
5
Span length [m]
Ab
utm
en
t jo
int
she
ar
forc
e [
N/m
]
a)
P02
P04
P06
P08
P10
Capacity: 110 kN/m
5 10 15 20 25 300
2
4
6
8x 10
5
Span length [m]
Pie
r jo
int
she
ar
forc
e [
N/m
]
b)
P02
P04
P06
P08
P10
Capacity: 220 kN/m
5 10 15 20 25 300
2
4
6
8x 10
5
Span length [m]
Pie
r jo
int
she
ar
forc
e [
N/m
]
c)
W20 S2
W14 S2
W08 S2
W20 S4
W14 S4
W08 S4
5 10 15 20 25 300
2
4
6
8
10
x 105
Span length [m]
Ab
utm
en
t jo
int
she
ar
forc
e [
N/m
]
d)
P02
P04
P06
P08
P10
Capacity: 110 kN/m
PMG PMG
PMG
Slab
Fig. 10 Resultant joint shear forces of (normalized to deck width): a) at the abutment (W14S4 PMGconfigurations); b) at the pier (W14S4 PMG configurations); c) for different deck widths (PMGbridges); d) at the abutment (W14S4 slab bridges)
where n, D and fsd are the number, diameter and design strength of the rebars; fcd is thedesign strength of the concrete and γR is the safety factor of 1.3. A conservative estimationconsidering C20/30 concrete and S500B rebars lead to a normalized resistance of ∼110 kN/mat the abutment (with φ16/150) and ∼220 kN/m at the piers (with 2φ16/150), in case ofPMG bridges. The resistance at the abutment is definitely insufficient even for shorter spans.The lower demands and the higher resistance of the pier joint lead to a lower vulnerability(critical only at shorter piers). Note, however, that after a possible failure of the abutmentjoint, redistribution of the forces may risk the failure of this component as well.
Normalized abutment joint shear forces (Fig. 10d) indicate that this component may becritical for slab bridges as well. Using Eq.(2) to calculate the resistance of a typical jointwith φ16/150 shear reinforcement results in ∼110 kN/m shear capacity showing that thereis a high probability that this component fails even in case of shorter spans. The deck topier joints are less vulnerable due to the lower shear forces, besides, it can be shown thatpier shear failure is much more likely to occur prior to the failure of the monolithic joint. Forinstance, if a typical slab bridge is considered (W14S4P06L25), the shear forces associatedwith cracking of the joint is two times larger than the pier shear resistance.
5.3.3 PiersResults for the PMG piers are depicted in Fig. 11a-c. Demands are lower in the longitu-
dinal direction which stems from the longitudinal support provided by the high stiffness ofthe abutment and the backfill soil. The longitudinal shear forces (Vx), the corresponding My
bending moments and the transverse shear forces (Vy) have the same tendency (Fig. 11a) ofbeing increased for shorter piers. However, in Fig. 11b, the maximum values of transversebending moments (Mx) do not correspond to the lowest 2 m pier height, instead, a peak canbe observed at 4 m. The pier height does not only influence the relative stiffness and thusthe transferred lateral forces, but also the lever arm of these forces. The pier should be highenough to minimize the developing seismic shear forces in a way that the governing bendingmoments are decreased as well.
The required shear reinforcement (Aw/sw) and the flexural DC ratio are calculated per
Seismic evaluation of highway overpass bridges 13
EC2-2 (CEN 2009b) and EC8-2:
Aw/sw = γBd · VEd/(z · fwd · cotθ) (3)
DC = (MxEd/MxRd)a + (MyEd/MyRd)
a (4)
where γBd is a partial factor of 1.25 for brittle failure; VEd is the resultant shear force; zis the lever arm of internal forces; fwd is the design strength of the stirrups; θ is the angleof the concrete compression strut; MxEd, MyEd and MxEd, MyRd are the design momentsand flexural resistance in each direction and the exponent a takes into account the normalforce in the element. Typical cross-section and material properties (0.6x0.9 m cross section;φ12/150 stirrups (∼1500 mm2/m); ∼1% longitudinal reinforcement ratio (16φ20); S500Bsteel and conservative concrete grade C20/30) are used for the calculations. According toFig.11c short piers show high vulnerability against shear forces (maximum applicable spanlength is <10 m), while flexural behavior is inadequate for higher piers (but the span lengthcan be much longer <17 m in this case).
5 10 15 20 25 300
5
10
15x 10
5
Span length [m]
Pie
r V
x,V
y [N
] a
nd
My
[N
m]
a)
P02 Vx
P02 Vy
P02 My
P10 Vx
P10 Vy
P10 My
510
1520
2530
24
68
100
0.5
1
1.5
2
x 106
Span length [m]Pier height [m]
Pie
r M
x [N
m]
b)5 10 15 20 25 30
0
1500
3000
4500
6000
Re
qu
ire
d s
he
ar
rein
forc
em
en
t [m
m2 /m]
Span length [m]
c)5 10 15 20 25 30
0
1
2
3
4
Fle
xura
l D/C
ra
tio
[−
]
P02 Shear
P10 Shear
P02 Flex.
P10 Flex.
Capacity
5 10 15 20 25 300
1500
3000
4500
6000
Re
qu
ire
d s
he
ar
rein
forc
em
en
t [m
m/m
]2
d)5 10 15 20 25 30
0
1
2
3
4
Fle
xura
l D/C
ra
tio
[−
]
Span length [m]
P02 Shear
P10 Shear
P02 Flex.
P10 Flex.
Capacity
PMG PMG
PMG
Slab
Fig. 11 Results for W14S4 configurations: a) pier shear forces (Vx,Vy) and vertical bending moments(My) (PMG); b) pier transverse bending moments (Mx) (PMG). Required shear reinforcement andflexural DC ratio of the pier: c) PMG bridges; d) slab bridges.
Slab bridge piers show higher vulnerability than PMG bridges against shear forces andflexural failure as well (Fig. 11d). The maximum applicable span length for short piers isunder 8 m, for instance.
5.3.4 PilesThe pile foundation is incorporated in the model with simple integrated springs. Detailed
analysis of the individual piles is out of scope in this study, however forces transferred tothe pile head can be calculated using the foundation layout and the reaction forces. Pilenormal forces are calculated to estimate whether compressive resistance failure occurs. Thetypical pile resistance is around 2000-2500 kN; therefore Fig. 12a-b confirm that failure isnot expected except for slab bridges with extremely short piers and long spans, which is arare configuration.
14 J. Simon and L.G. Vigh
5 10 15 20 25 300
0.5
1
1.5
2
x 106
Span length [m]
Pil
e f
orc
e [
N]
a)
P02 Ab.
P02 Pier
P10 Ab.
P10 Pier
10 20 300
100
200
300
Pa
ssiv
e e
art
h p
ress
ure
[k
Pa
]
Span length [m]
c)10 20 30
0
5
10
15
Ma
x lo
ng
. dis
p. [
mm
]
P02 dx
P10 dx
P02 Press.
P10 Press.
5 10 15 20 25 300
0.5
1
1.5
2
2.5
3
3.5x 10
6
Span length [m]
Pil
e n
orm
al f
orc
e [
N]
P02 Abut.
P10 Abut.
P02 Pier
P10 Pier
b)10 20 30
0
100
200
300
Pa
ssiv
e e
art
h p
ress
ure
[k
Pa
]
Span length [m]
d)10 20 30
0
5
10
15
Ma
x lo
ng
. dis
p. [
mm
]
P02 dx
P10 dx
P02 Press.
P10 Press.
PMG
PMG
Slab
Slab
Fig. 12 Results for W14S4 configurations. Pile normal forces: a) PMG bridges; b) slab bridges.Maximum earth pressure and maximum longitudinal displacements: c) PMG bridges, d) slab bridges.
5.3.5 Abutment and backfill soilTwo other components, the abutment and backfill soil demands are shown in Fig. 12c-d.
The abutments are considered as rigid blocks, therefore only global stability failure is takeninto consideration. Demands are determined as the maximum longitudinal displacementthat can possibly cause stability failure, while the backfill soil demands are measured withthe maximum passive earth pressure. These demands are in high correlation, since passiveearth pressure is caused by the longitudinal movements of the abutment. It can be con-cluded that the probability of failure is low. Passive earth pressure never reaches ∼430 kPa(ultimate failure threshold per Caltrans), while the displacements are always under 30 mm(recommended limit for bridges of importance class III per EC8-2).
5.4 Critical components and layouts
To highlight critical components and layouts, maximum acceptable PGA (MAPGA; DCratio is divided by the applied PGA value) is calculated for each component of each configu-ration. The capacities of the components are the ones presented in the previous subsections.Fig. 13 presents the dependency of MAPGA on the pier height and deck width in case ofPMG bridges. The pier height highly influences the pier internal forces (especially shear),thus the MAPGA values as well (Fig. 13a-b). As confirmed by Fig. 13c-d, the results areless sensitive to the deck width, pier height and the length of the superstructure are far moreimportant structural attributes.
It is assumed that the failure of one component can initiate the failure of the whole system(series system). It is important to understand which component is the most vulnerable fordifferent layouts. In Fig. 14, MAPGA results for the most vulnerable components areillustrated for W14S3 PMG configurations. High vulnerability of the abutment joint isconfirmed, this component is the most critical for every configuration. Failure of the pieris characterized by shear or flexural failure for shorter or higher piers, respectively. Notethat flexural capacity can be characterized with at least a limited ductile behavior. Thisindicates the sensitivity of piers to shear forces for pier heights (5-6 m) typically used in caseof highway bridges.
Seismic evaluation of highway overpass bridges 15
10 20 300
1
2
3
4
5
Span length [m]
MA
PG
A [
m/s
2]
a)
P02P04P06P08P10
10 20 300
1
2
3
4
5
Span length [m]
MA
PG
A [
m/s
2]
b)
P02P04P06P08P10
10 20 300
1
2
3
4
5
Span length [m]
MA
PG
A [
m/s
2]
c)
W08W14W20
10 20 300
1
2
3
4
5
Span length [m]
MA
PG
A [
m/s
2]
d)
W08
W14
W20
Fig. 13 MAPGA values of S3 PMG bridges. Different pier heights (W14): a) pier bending; b) piershear. Different widths (P06): d) pier bending; e) pier pile compression. Typical moderate PGArange: 1-2 m/s2.
10 20 300
1
2
3
4
5
Span length [m]
MA
PG
A [
m/s
2]
a)
B1PMPV
10 20 300
1
2
3
4
5
Span length [m]
MA
PG
A [
m/s
2]
b)
B1PMPV
10 20 300
1
2
3
4
5
Span length [m]
MA
PG
A [
m/s
2]
c)
B1PMPV
Fig. 14 Critical components for W14S3 PMG configurations: a) P02; b) P06; c) P10. (B1-abutmentjoint; PM – pier flexural failure; PV – pier shear failure). Typical moderate PGA range: 1-2 m/s2.
Table 5 MAPGA values for pier flexural and shear failure of W14S4 bridges.
MAPGA values are calculated for slab bridges as well. The dependencies on the deckwidth and pier height are similar to those presented in Fig. 13 in case of PMG bridges,while the critical components are also identical for the same configurations. However, pier
16 J. Simon and L.G. Vigh
internal forces are generally higher in case of slab bridges for the same arrangement dueto the different monolithic joint Type 1, transferring not only shear forces but also bendingmoments. Besides, the mass of the slab bridges is also higher causing higher seismic demands.Table 5 illustrates the differences in MAPGA values related to pier flexural and shear failureof W14S4 bridges. Worse performance can be observed for both bridge classes if the piersare shorter and the spans are longer. Note the better performance of PMG bridges for atypical highway overpass configuration (P06 and L20-25).
6. Nationwide seismic performance evaluation
A possible application of the parametric results is illustrated through the example of anationwide seismic performance evaluation in Hungary as follows:
1. Essential parameters of a specific bridge are obtained from the Hungarian road bridgedatabase (HTA 2016) (bridges without sufficient input parameters are excluded).
2. MAPGA values are determined with linear interpolation on the parametric results foreach structural component.
3. MAPGA values are modified with a factor reflecting bridge condition (the existingbridge database employs a 5 level scale with 1 being excellent condition and 5 beingextensive damages; from condition 1 to 5 a factor of 1.0-0.6 is applied).
4. PGA value for the bridge site is determined using the seismic zonation map of Hungary(Toth et al. 2006).
5. DC ratio of each component is calculated comparing the PGA and the correspondingMAPGA.
To illustrate the utilization of each bridge component regarding all the examined bridges,empirical cumulative distributions (representing non-exceedance) of the component DC ra-tios are created (Fig. 15). For example, the B1 curve in Fig. 15a shows that the abutmentmonolithic joint is critical for ∼20% of single span bridges, while the PV curve in Fig. 15bindicates that ∼30% of the multi-span bridges have inadequate pier shear resistance.
Fig. 15 Critical bridge components of a) single and; b) multi-span bridges.
Seismic evaluation of highway overpass bridges 17
In case of single span bridges only the abutment joint is critical. In 22% of the observed1313 bridges, there is a possibility that this component fails (Table 6). The percentageis lower for slab bridges, for they are often constructed for shorter spans. Failure of thiscomponent is highly probable for multi-span bridges as well, more than 90% of the bridgeshave inadequately detailed abutment joint.
Table 6 Relative number of critical bridge components.
Single span bridges Multi span bridges
Abutment joint Total number Abutment joint Pier flexural Pier shear Total numberPMG 29% 758 94% 1% 22% 602Slab 12% 555 96% 4% 51% 166ALL 22% 1313 95% 2% 28% 768
The joint failure does not necessary cause progressive collapse in case of multi-spanbridges; pier failure is far more dangerous. Table 6 also shows the relative number of bridgeswhere collapse occurs either with pier flexural or shear failure. According to Table 6, piershear failure is critical for the most commonly used typical highway overpass layout (P06 andL20-25). This is reflected in the results: pier shear failure is more likely to occur regardingthe whole bridge stock. Note also that a significant portion of slab bridges may suffer pierfailure even though they are usually constructed with shorter spans. It should be emphasized,however, that these results are obtained with conservative assumptions (both for capacitiesand demands), thus the number of critical structures may be lower in reality.
a) b)
CriticalAdequate
Fig. 16 Critical bridges. a) Single span - abutment joint failure. b) Multi span - pier failure.
In Fig. 16, single span bridges with possible abutment joint and multi-span bridges withpier failure (causing progressive collapse) are illustrated. These maps are useful tools toidentify critical bridges and to select regions of interest for a possible retrofitting project.
7. Conclusions
Precast multi-girder and slab bridges have a significant contribution to typical bridgeinventories. Most bridges were non-seismically designed in several moderate seismic areas;the seismic behavior of these structures is not known. A parametric seismic analysis iscarried out to examine the seismic behavior and to determine possible critical componentsand layouts. The following conclusions are drawn from the results:
• Modal analysis confirms that these structures are relatively stiff, the fundamental pe-
18 J. Simon and L.G. Vigh
riod often falls onto the plateau of the applied response spectrum.
• Investigation of the effect of the soil-structure interaction concludes that internal forcesand displacements are highly dependent on the relative stiffness values of the SSI com-ponents. The analysis should be carried out taking into account conservative stiffnesscombinations for each bridge component.
• Due to the integral construction, longitudinal movements of the piers and abutmentscause vertical bending in the superstructure; relatively high bending moments developthat are comparable with (or even higher than) those caused by vertical vibration.This phenomenon is more dominant if the span number is even (e.g. 4-span bridges).However, it is also shown that the superstructure is likely to be adequate even thoughit is designed only for ULS combinations.
• Seismic demands are increasing with bridge length, while monolithic joint shear forces,pier demands highly, foundation normal forces moderately, abutment and backfill-soil demands slightly depend on pier height. The deck width is a far less importantstructural attribute regarding the seismic behavior.
• The failure of the abutment and the backfill soil is not expected; it is also shown thatpile compressive resistance is adequate in case of typical bridge layouts.
• Single-span bridges are less vulnerable, however failure of the abutment monolithicjoint may occur.
• Longer multi-span bridges are more vulnerable, the most critical component is theabutment monolithic joint. Note, however, that progressive collapse is initiated withthe failure of the piers, which can be characterized as expected: shorter piers suffershear, while higher piers suffer flexural failure.
• Piers can be characterized with at least a limited flexural ductility, thus the resultshighlight the high vulnerability of piers to brittle shear failure.
• Observing multi-span configurations in a typical bridge inventory, it is found that 30%of the bridges may suffer pier failure, which implies significant economic consequences.
Although the accuracy of the adopted method is insufficient for estimating the extentof damage, it provides a realistic basis for assessing the overall seismic performance. Sucha preliminary parametric analysis can allow us to sketch the most vulnerable componentsand layouts, therefore to improve the knowledge on and the prevention of the seismic riskat a national scale. The results enable the authorities to decide about future actions: e.g.to elaborate risk prevention plans and retrofit priorizations. The illustrated preliminaryparametric seismic analysis approach can be efficiently used for: 1) further detailed seismicassessment and risk based seismic analysis; 2) retrofit planning for the critical bridges; 3)development of design concepts of newly built structures in moderate seismicity areas.
Seismic evaluation of highway overpass bridges 19
Acknowledgements
This paper was supported by the Janos Bolyai Research Scholarship of the HungarianAcademy of Sciences. The authors highly appreciate the help of the members of the Hun-garian Transport Administration, who provided the bridge database and gave instructionsabout its structure and application.
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